Problem: Divide. Write the quotient in lowest terms. $3\dfrac{1}{8} \div 1\dfrac23 = $
Explanation: First, let's rewrite $3\dfrac1{8}$ and $1\dfrac23$ as fractions: $3\dfrac{1}{8} \div 1\dfrac23 =\dfrac{25}{8} \div \dfrac{5}{3}$ [How do we write a mixed number as a fraction?] Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{5}3$ is $\dfrac3{5}$. Now, we can rewrite our expression as a multiplication problem: $\dfrac{25}{8} \div \dfrac{5}3=\dfrac{25}{8}\times\dfrac3{5}$ $=\dfrac{25\times 3}{8\times 5}$ $=\dfrac{ \stackrel{5}{\cancel{25}} \times~ 3 }{ 8\times\underset{1}{\cancel{5}}} $ $=\dfrac{5\times 3}{8\times 1}$ $=\dfrac{15}{8}$ We could also write this as $1\dfrac7{8}$.